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J.K. Lawrence, A.C. Cadavid (CSUN), A.A. Ruzmaikin (JPL)
Many solar phenomena display a scaling symmetry associated with random multiplicative cascades. Here a physical measure, initially uniform on a spatial, temporal, or space-time set, is divided among subsets according to randomly determined fractions. This division is repeated on smaller and smaller sub-subsets, so that the resulting measure at the smallest scale is given at any point by the product of a string of random fractions comprising its fragmentation history. Such measures are highly intermittent. They characterize such solar phenomena as the spatial distribution of magnetic flux in an active region and the time distribution of global X-ray emission.
The probability distribution functions (PDFs) governing the random fractions fall into universality classes with robust properties (Hentschel 1994). For example, all PDFs which allow for zero fractions lead to measures with local peaks of unlimited strengths which are progressively less and less space filling. The GOES-2 X-ray data belong to this class, which indicates the presence of critical behavior associated with flares (Lu & Hamilton 1991). We investigate a number of time series for the presence or absence of this property.
Multifractals in nature may fall into a narrow universality class described by just 3 parameters (Schertzer, et al. 1997). We find that at least some examples of active region magnetic fields do indeed have the conjectured form. Further, we apply a causal space-time version of this class of multiplicative cascade processes to forecasting the evolution of solar velocity fields.
This work was supported in part by NSF grant ATM-9628882.
Hentschel, H.G.E. 1994, Phys. Rev. E, 50, 243. Lu, E.T. & Hamilton, R.J. 1991, ApJ, 380, L89. Schertzer, D., Lovejoy, S., Schmitt, F., Chigirinskaya, Y. & Marsan, D. 1997, Fractals, 5, 427.
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